Two Weeks in Eastern France and Western Germany

Lyon kind of sticks out like sore thumb, but that is OK, it is still very doable by train. Go Paris to Lyon (2 hr) to Strasbourg(3 hr) to Baden-Baden(1/2 hr) to Rothenburg to Bacharach to Frankfurt airport.
The first 3 legs can be done with direct TGV trains way faster than any car.
Baden-Baden to Rothenburg and Rothenburg to Bacharach will require at least 3 train changes and take over 4 hours, but that is the way it is. Rothenburg is kind of out on a little branch line. Bacharach to Frankfurt airport is a 1 hour direct train in the morning.

I'd check airfares into Lyon as well as Frankfurt and Paris. If Paris isn't on the target list for this trip, I wouldn't fly into that city unless it made financial sense. (I realize that for Lyon you're likely to have to change planes in Paris.) And I wouldn't fly in and out of the same city since your itinerary doesn't look like a loop trip to me. Probably into Lyon or Paris and out of Frankfurt.

You can check travel times by train easily on the Deutsche Bahn website, though for fares within France you'll eventually need to go to SNCF. It's too early at this point to see precise schedules for your travel dates, but you should be able to get a very good idea by checking April dates. At a quick glance I see that Lyon-Strasbourg tickets can cost between 33 euros and 77 euros (or perhaps less/more), depending on how far in advance they are purchased. (Beware the routings that require you to take a costly TGV into Paris and another costly TGV back out to Strasbourg.) The cheap tickets are not changeable or refundable.

The train will be faster than driving between Lyon and Strasbourg, and you won't want to use a car within either of those cities. South of Strasbourg, however, there are a bunch of cute little wine towns, and a car will improve your flexibility in seeing them. Some do have rail and/or bus service. Colmar (highly recommended) in particular is readily accessible by train from Strasbourg. If your focus in this area is wine, you might consider staying in Colmar instead of Strasbourg. I think it would be a bit more convenient, geographically, and I suspect you'd save on hotel costs (though I haven't verified that).

You'll want to drop the French car, if you rent one, somewhere on the French side of the border to avoid a probably-grotesque international drop charge. Our German experts can provide guidance on whether a car will add much, or any, value of the second part of your trip.

If you make no changes to your itinerary, it looks to me like the logical order is Lyon - Strasbourg - Baden-Baden - Rothenburt odT - Bacharach, assuming you fly out of Frankfurt. If you find you can save a lot of money by returning from Munich instead, you'd want to reverse Rothenburg and Bacharach. You could, of course, reverse the order completely and fly into Germany, out of France. Weather-wise, I doubt that it matters, so I suggest doing some Googling (and guidebook reading) to see whether there are special events you'd like to hit--perhaps something wine-related?

You can avoid that awkward jog east to Rothenburg by asking our German pros to suggest equally charming towns that are much closer to Baden-Baden and Bacharach.

I see no reason to fly any part of your itinerary.

Having lived in the Frankfurt area for a couple years and made the trip many many times from Wiesbaden to Rothenburg ob der Tauber and Bacharach, car or train are equally viable options for these two towns.

Rothenburg odT
Driving
2.5 hour drive from Frankfurt area going through the beautiful city of Würzburg. I'd recommend just skipping the backroads and getting the drive over with by sticking to the autobahn if you're on a tight schedule. Parking is super easy in Rothenburg at just a few Euros for the day. The altstadt (old city) part of Rothenburg is entirely walkable literally within nothing more than 5 minutes away in any direction. Highlights are walking the city wall, Christmas museum and the Käthe Wohlfahrt store (unless you hate Christmas), seeing the clock tower in the town square at the top of the hour, the Middle Ages Crime & Punishment museum and honestly the best part, the Night Watchman's Tour. Seriously, the Night Watchman's Tour is excellent and worth the trip alone. Consider that it's an hour long starting at 8pm, if aren't staying in town at a hotel you'll have to do the 2+ hour trip back arriving back in Frankfurt around midnight. Not sure if the train even departs that time of night for Würzburg and eventually Frankfurt.

Train
If you take the train from Frankfurt you'll board the ICE (bullet train) for a very quick trip to Würzburg, change trains to an S-Bahn regional train and arrive in downtown Rothenburg relatively close to the altstadt area, only a couple minutes walking. In my opinion if you take the train, plan on staying overnight since leaving late might not be an option.

Bacharach

Driving from Frankfurt to Bachrach requires crossing the bridge in Mainz since there are no bridges crossing the Rhine between Mainz and Koblenz. So driving to Bacharach is a bit out of the way compared to what it looks like on a map. Easy drive though and just over 1 hour from Frankfurt to Bacharach. Parking is super easy along the main road (parking meters) right by the ferry terminals. Walk just across the road and under the train tracks and you're in the heart of Bacharach. See Rick Steve's book for the highlights... all worth seeing.

Taking the train is somewhat just as easy with a stop most likely in Mainz, change trains and continue onto Bacharach (another 30 minutes or so).

A day trip out to the Moselle River to see Burg Eltz http://burg-eltz.de/en/ and the little town of Cochem might be worth consideration, especially if you're driving. The Moselle River and the wineries along it are some of the finest in the world with beautiful views all along it.

You might check Lyon's Saint-Exupéry's airport website for fares flying directly to Lyon. They seem to be offering a promotion, with several fares under $1,000 from selected North American airports.

Website is https://www.lyonaeroports.com/en/

Could be cheaper than a flight to Paris + TGV to Lyon.

Personally I think Rothenburg is too far a distance to be worthwhile. There are plenty of attractive, heavily-touristed towns in the Mosel valley to visit instead that wouldn't need such a long journey.

We lived in Augsburg, Germany near Munich for four years when the US Army was still protecting W. Germany from the huge Soviet Army, then the wall came down and most of the Army went home.

We have traveled all over the places that you want to visit.

Rothenburg on the Tauber is wonderful and on the Romantic Road. I suggest that you plan on doing the entire road, since there are many other notable places to see. There are tours from Munich for the Romantic Road. You could fly into Munich do the Munich area, go to Garmisch then do the Road.
From Bavaria, then head to the Black Forrest and see Baden Baden, Friberg and Triberg. It time, see the Rhine Falls into the Bodensee.

Strassbourg, France is good. Lyon is on the Rhone, which should be done all the way to the Med. Perhaps you don't have time. I suggest you save Lyon for doing that later.

As others have suggested, do open jaw, flying into Munich, fly out of Zurich, Frankfurt or Paris.

"As of now we're looking at Lyon, Strasbourg, Baden Baden, Bacharach, and Rothenburg..."

You're looking to see "a gorgeous region of Europe" but I think your itinerary is missing much of the beauty. Bacharach indeed is in one of Germany's most scenic regions. But I think you ought to reconsider using all these German towns as anchors for your itinerary. As others indicate, Rothenburg is an outpost on a distant frontier - it's also a tourist magnet extraordinaire. Even Rick Steves' website article on R'burg admits that "Rothenburg is well on its way to becoming a medieval theme park." Casinos and spa treatments are the draw in Baden-Baden, alright if that's what you're looking for, but it works very poorly as a "Black Forest village" if that's what you were thinking. Note that B-B is a poor train base for outings as well because the station is so far outside town. (You might keep Bacharach, but there are several great old-world towns on the Rhine that work somewhat better as travel bases for the Rhine/Mosel region.)

Have you taken a look at the Neckar River Valley?? In most of these places you will more often find gorgeous natural scenery and more "Germany" than in your previous choices...
Hirschhorn
Neckar Magazine guide

The above guide mentions Villingen-Schwenningen - the eastern gateway to the Black Forest and a great place to hop on one of Germany's most scenic railways, the Black Forest Railway. Check out the BF town links at the page below...
https://www.black-forest-travel.com/places-of-interest/black-forest-railway.html
...and these links as well...
train ride photos to click through
Gutach
Gengenbach

Philip mentions the Mosel Valley - it's "next door" to the Rhine, so don't miss it.
Cochem
Mosel Highlights
Mosel train route

The BF Railway ends in Offenburg - just a stone's throw from STRASBOURG - and it's very convenient to get there by train.

Thanks so much for the great recommendations! Lyon is kind of the one place we HAVE to go as we're meeting some friends there for 4 nights, but we're happy to time that at either the beginning or end of our trip. We have found that it's cheaper for us to fly in and out of the same airport (Paris being the cheapest at the moment, but I have seen some really inexpensive flights in and out of Lyon as well). With that said, I understand that sometimes the added cost of getting back to that original airport with trains, hopper flights etc. more than makes up for the difference, and am open to Frankfurt or Munich as an option (both for travel and to visit...any suggestions there? Do you any of you like those cities to visit/stay in?). Strasbourg was another one we were really hoping to hit as I've heard great things about it (namely that it's the perfect combination between French and German cultures and cuisine). Just some background...I used to live in Paris, and was just there with my husband this past September for quite some time (which is why we hadn't planned on staying there for a chunk of this coming trip). I speak French well and am a chef so food is naturally very important to us (as well as history, architecture, art, culture, etc.).

Yes, fly back from Frankfurt airport as it is just a 1 hour train from your last stop in Bacharach. You can go straight to the check in from the airport train station.

Oh and I really love the suggestions for where to stay instead of what I had mentioned! The options I stated were just ideas. We were kind of hoping to hit up one town in the Black Forest and one town in the Rhine area, but really, we are flexible as long as we make it to Lyon at some point in the journey (as I mentioned in my previous reply, we're meeting friends there for 4 nights).

We have a number of people on this forum (I'm not one) who are super-knowledgeable about Germany and can give you wonderful advice about great places to visit that don't require zipping back and forth across the country hitting an isolated spot here and there. I am a huge fan of going to an area with a lot of attractive towns and small cities and staying there. It really keeps the transportation costs down.

Alsace as a whole is a blend of France and Germany. I find the architecture really beautiful. The historic section of Strasbourg is lovely (I was there 25 years ago), but it's a large city that I assume has major traffic issues; probably not a place to stay if you are currently encumbered with a car. I suspect the hotel rates there are higher than in surrounding areas, though I haven't verified that. If you're training it, I believe Strasbourg is the quickest Alsatian to reach from Lyon (TGV service), which is a major advantage.

Last summer I stayed in Colmar, a much smaller (but also touristy) town that would be more manageable with a car, I think. There are lots of pretty little wine villages nearby, and Colmar has a fabulous museum, the Unterlinden, to go along with the beautiful houses and canals. I typically don't have a lot of patience for the most touristy of the smaller places (Rothenburg, though gorgeous, is well over the line for me), but Colmar is just.so.pretty. And it's large enough that you can walk away from the throngs if you want to.

Personally, I find Alsace more superficially engaging than Munich, but Munich has some important museums and historic sights. Not enough to drag me all the across the country, though, with so many interesting places along the way. I'd hold off on Munich for now and include it on a later trip, perhaps along with Leipzig, Dresden, Erfurt and the time-sink that is Berlin. Plus some of the gorgeous smaller towns in eastern Germany, of course. Really, there are just too many places.

Lyon is great, by the way. Very handsome city and one with a lot of things to see.

Back to your original itinerary, fly into Paris. Then head to Lyon, its only 2 hours away on frequent TGV's. There are several direct TGV's from Lyon to Strasbourg, the fastest one (fewest stops) in the 8:34 one getting to Stasbourg at 11:44. I haven't checked, but it is probably the most expensive as well. Something about Strasbourg being them home of the European Parliament.

So after that, you're pretty free to come up with an itinerary that suits you. Since you'll be traveling mostly on regional trains in that area, you could even play it by ear to a certain extent. I still think flying back from Frankfurt works best for you. Black Forest, Rothenburg, Rhine Gorge are all nearby.

Thank you again for all the fantastic recommendations! What is the best town to stay in as a base for exploring The Black Forest region? Could we possibly see some of the Black Forest highlights from Strasbourg as day trips? And what would be your recommendations for the best place to anchor ourselves to explore the Rhine or Mosel valleys?

Another option to throw into the mix...a friend suggested we train from Lyon to Zurich and then venture northward into Germany that way. My husband and I actually don't mind larger cities (we love Rome, London, and Paris), but hadn't originally considered it for this particular trip.

Check rail fares for the route that goes through Switzerland. It might be much more costly.